Needing 341 more runs to win the Colombo Test with eight wickets in hand, Sri Lanka will resume their second innings on Monday from their overnight score of 72 for 2 on the fifth and final day.
At the draw of stumps on Sunday, Dimuth Karunaratne on 25 and Skipper Angelo Mathews on 23 were at the crease.
Veteran wicket keeper batsman Kumara Sangakkara scored 18 in his final international cricket innings. The other wicket to fall to the Indians was that of opener Kaushal Silva.
India had earlier declared their second innings at 325 for 8, setting a target of 413 for Sri Lanka to win this penultimate Test and clinch the three-match series.
Ajinkya Rahane made 126, while Murali Vijay was the second highest scorer with 82.
Vijay and wicket keeper Wriddhiman Saha have been ruled out of the remainder of the series due to hamstring injuries. Naman Ojha and Karun Nair have been named as their replacements.
The final Test will be played at Colombo from August 28.